I don't think putting an AI button on is really that useful for enhancing game play.
With respect to making grinding for cards more fun / less time consuming, I think the best thing would be to raise the reward for bronze league slightly since right now it returns less per win then you lose per loss. As it is now, its almost a waste of time to play it since for a win you only get back a little over a quarter of what you lose if you dont win. can get better return from lvl2 or lvl3 ai and don't have to face a bumped up opponent. (no extra hp or chance of upgraded cards). Raising it to something between 10 and 30 might make it more worthwhile.
As for using it to watch the AI play, I think just watching, say, a lvl 3 ai play your deck isn't too interesting. I think a better option would be to let people watch Arena battles if this is what you are after.
What might be interesting, though, is to allow players to create a custom AI to go with a deck they construct and allow them to use it in a seperate AI pvp mode. Then players can watch their creations duke it out in a duel
. This could also be a useful addition to the arena.
This would probably be more interesting if there were a bit higher degree of "hidden information" in the game. I.e. more facedown / invisible type mechanics to make building a good AI a challenge.
Of course, implementing a safe, not too buggy programmable AI may take quite a bit of work in coding though.